The dynamics of two chemically similar type-A polymers, poly(epsilon-caprolactone) (PCL) and poly(lactic acid) (PLA) with small amounts of Cloisite 30B nanoplatelets were investigated via broadband dielectric relaxation spectroscopy. The terminal relaxation, or normal mode of PCL was found to be strongly influenced by the presence of the nanoplatelets, exhibiting a relaxation from PCL chains within the Cloisite platelets as well as a bulk-like relaxation. These results, as well as rheological and X-ray scattering results from the literature, help to form a clearer picture of how the structure and dynamics relate to the bulk physical properties in these systems. Cloisite was observed to have minimal impact on both the glassy state dynamics, as well as the segmental dynamics of both polymers, due to the relatively weak interactions between the polymers and the platelets.